Method and apparatus for precisely contouring a workpiece imprecisely positioned on a supporting fixture

ABSTRACT

Method and apparatus for manufacturing precisely dimensioned metal parts on a program-controlled machine tool having a workpiece-supporting fixture, without the necessity of precisely locating the workpiece on the fixture. The workpiece is first placed on the fixture in an approximate position within predetermined limits of a standard position. The actual position (i.e., location and orientation) of the workpiece on the fixture is then measured by means of a programmed measuring apparatus while the fixture is accurately located with respect to that apparatus. The machine tool is controlled by a standard program, based on a standard position of the workpiece on its fixture and an accurate location of the fixture on the machine tool. The data defining the actual position of the workpiece on the fixture are utilized to modify the program of the machine tool, so as to compensate for the difference between the standard position of the workpiece and its actual position. The measurement of the workpiece position is performed at a measuring station, and the fixture with the workpiece mounted thereon is then conveyed to a fabrication station, which is shown as including a numerically controlled five-axis machine tool. The position-defining data determined at the measuring station is associated with identifying data of the particular fixture and is stored in a memory. When that fixture arrives at the fabrication station, it is accurately located with respect to the machine tool, and is identified. The identifying data is used to retrieve from the memory the proper set of position-defining data, which is used to modify the machine tool program to produce the desired precisely dimensioned product.

United States Patent Armonk, N.Y.

Appl. No. Filed Patented Assignee [54] METHOD AND APPARATUS FOR PRECISELY CONTOURING A WORKPIECE IMPRECISELY POSITIONED ON A SUPPORTING FIXTURE 13 Claims, 30 Drawing Figs.

U.S. Cl ..235/ll.ll,

33/174, 90/D1G. 27, 318/574, 340/172.5 Int. Cl G051! 5/00, G06f /18, B23q 5/22 Field ofSearch ..235/151.l1; 340/1725; 318/567-574 [56] References Cited UNITED STATES PATENTS 1/1965 Rosenberg 235/151. 1/1966 Lemelson..... 235/151. 4/1967 Lemelson..... 235/151.ll 1/1970 Stobbe 235l151.l1

OTHER REFERENCES Tape Controlled Transfer Machine Automation, June 1958 p. 34- 39.

Measurement Made Easy Metalworking Production, Jam,

X X X X Primary Examiner-Eugene G. Botz Assistant Examiner-Felix D. Gruber Anorneys--Hanifin & Jancin and Graham S. Jones, 11

ABSTRACT: Method and apparatus for manufacturing precisely dimensioned metal parts on a program-controlled machine tool having a workpiece-supporting fixture, without the necessity of precisely locating the workpiece on the fixture.

The workpiece is first placed on the fixture in an approximate position within predetermined limits of a standard position. The actual position (i.e., location and orientation) of the workpiece on the fixture is then measured by means of a programmed measuring apparatus while the fixture is accurately located with respect to that apparatus. The machine tool is controlled by a standard program, based on a standard position'of the workpiece on its fixture and an accurate location of the fixture on the machine tool. The data defining the actual position of the workpiece on the fixture are utilized to modify the program of the machine tool, so as to compensate for the difi'erence between the standard position of the workpiece and its actual position.

The measurement of the workpiece position is performed at a measuring station, and the fixture with the workpiece mounted thereon is then conveyed to a fabrication station, which is shown as including a numerically controlled five-axis I machine tool. The position-defining data determined at the measuring station is associated with identifying data of the particular fixture and is stored in a memory. When that fixture arrives at the fabrication station, it is accurately located with respect to the machine tool, and is identified. The identifying data is used to retrieve from the memory the proper set of 1964, p. 45- 49. position-defining data, which is used to modify the machine tool program to produce the desired precisely dimensioned product.

WORIPIECE IVTET\U REIVIE N I" l'liflfifl' 0 l FIXTURE 6 1 TYPE OF WORKPIECE F, g PRQGQAIII I m START 23 ELEME'IT I w 2 24 Err-x 4 l l l I [:39 II. .5. M. s. I Y m CONTROL I l cIIIIPuIII a- II W ELEMElT l I IFIss.I2I7I ELEMENT I l5, 5 I I FIXTURE I I IDENTIFIER I iT T T T T T 5 3 MEMORY m 1 FT a: 72 T-KB'REZTIQ STATION b x. i I II I 43 F.S. l l Iflpgwg Bl gh COMPUTING 00L 4 L- (LPLAFlE OF PAPER) F. S. M ELEMENT L X" DRIVE FOR CONTROL I 1 an 2943-" TOOL HOLDER ELEMENT f I ROTATION 2 F5 l AXIS DRIVE I fir: :I PROGRAM 1 T L T ELEMENT I a} FIXTURE 26 V I I IDENTIFIERJ/IH sum new 18 FIG. 2

' CENTER 0F mamas 4012 16331011 sum sun; 18

COORDINATES 0F ROTIATIOIIIV ARIEL c, c, c Z

mEmEnu am A .633.011 SHEET 050E 18 if LINE PARALLEL T0 AXIS Q A FIG. 8

LINE PARALLEL 9 Z"Y'-'PLARE I LLRE PARALLEL m X"AXIS AND CONTAINED lN X Y'-'PLANE /To=z"AxLs AND -CONTAINED IN m m 4m v FIG. |2

v v "3.633.011 *sum user 18 CLOCK FIG. FIG. 83

[2A mg \--82} 0R FROM FIG. |2e 9| STEP 0 START 9 7 wen swncn 90 v S'NGLE (F|G.l) STEP l /'9 To SHOT V smrz {ROM '9 2 UPPER um. N 55? I r m f STEP "3 FOR FROM END *READ IN AND. 5mg FIG..I6 {46 I STEP .4 RING F I G IN-X-POSITION V M I [5A 7 M8 V m X ,POSYITION STEP 5 ND V CONTACT 163 STEP s STEP 0 "2' 4 coum= m AND FROM m 9 I86 13A STEP PULSE AND v n60 55m l0 1 LIMIT comm 19: AND

GAGE SENSOR FROM 11 coum=o mo FIG. 13A v STEP |2-- 225 mom N0 RESIDUE AND V FIG. 14 1225 STEP '4 q I 255 FROM ACCEPT mm .FIG. l6 1 2 3 STEP 254 ACCEPT I AND STEP -|6 ACCEPT AND P ACCEPT v Amy STEP l8 FROM TRAVERSE 4 M0 FIG. l4

' manna-m .4192:

SHEET 07UF 18 as RING To IN NORMAL END OUTPUT 'Q FIGURE FIG. I2B

STEPO INDICATOR 2 BB I 93 I4 1 2 |0l,98 |3B,l4 v 3 mew |3A,|6 STEP 4 I59 |5A FROM 5 I50 I38 TA 2 FIG 5 TE 1 e I60,l6| 152,14 M STEP RING I 7 1 7 4 LINES INPUT I 8 [3B LABELLED FOR A8 sms STATE STEPI 9 "3,";9 BA |5A |N F|Gs RING 2. l0 m use m H n I93 [3A 2 I2 214 M. I I3 226,273,227 I4,I5A,|5B I I4 24| 242 I6 SET BUS I I5 256 Is I I6 252 l6 1? 2m I6 I I9 268 I4 85 ERROR END STEP 2o INDICATOR |ee EP 5 FROM 2 LOWER LIMIT AND SET 20 FIG. 13B H54 I RESIDUE STEP l2 s51 14 222 224 RING as 7 SET J STEP |a NOTXORY FINAL AND SET 6 2 FROM L 232 TIMING FIG. I4

x ORY FINAL AND SET L 240 7 STEP 18- 267 TRAVERSE -4 AND SET 0 244 STEP 9 2" sn 2 RESET AND SWITCH a2 FROM PROGRAM ELEMENT 22 (FIGJ) "SHEET 130E 18 SE SE S Y POSITION X-F|NAL Y FINAL DATA-IN BUS,

END READ- IN ml 1 241 25s I ACCEPT LEADING EDGE SET 0 ACCEPT on AND ACCEPT AND RESET A 25' 252 254 A 255 250' 22 [FROM FIG. 14 EQZ AAs. PROGRAM 3 F ,24| STEP l4 (LOAD-I) FROM STEP I5 (LOAD-2) m STEP l6 (LOAD-5) A COMPUT'NG STE I? (LOAD-4) ELEMENT (no.1) DATA -our BUS 42 2 24? FROM FIG. I28 STEP /2 7 GATE TRAvERsE coum FROM FIG. :4 244 BUS STEP l5 FROM F|G.|2B K \24a 245 24s FROM FIG ISA X BUS READOUT OR 251 BUS FROM FIG. 12B STEP Gm :45 FROM FIG. I5A Y READOUT BUS 26 A FIG. l6 FROM FIG. I2B STEP 2 A 250 GATE FROM FIG. I58 E BUFFER BUS mmtnmm 3.6337611 SHEET lHUF 18 RIN COU R PROGRAM PHASE STEP IDLE o INITIAUZE I 2 BEGIN NEW 3 SEARCH 4 5 a 'sEARcR FIG. I?

" s EERCE EQ \2 R l E DIAGRAM |4 TRANSFER .DATA T0 COMPUTING "l ELEMENT '9 ,l

ERROR 7 l i l 5 m l 8 8 x E, z J I I I 4 l u\ 6 I (gm Es z 4' l F'G. l8 3/ PATENTEDJAN 41912 31633011 SHEET lSBF 18 RAIEIIIEDII 4m:

SHEET 18 OF 18 IDENTIFY TYPE OF IIIDRIIPIEDE FIG. 22

I IDEN I .SELECT PROGRAM FIX FROM sIIIRIIcE 22 III.s.I

SEARCH FOR OATUM cDIIIouRs CONTOURS (COORDINATES 0F NOT FOUND POINTS II,R,s, II

( ERRDR I 'coIIIouRs FOUND COMPUTE POSITION DEFINING DENNY -FIXTURE IIIID DATA (P.D.D.) EOS.(I)TO (I5) IIITE (FIG. 25)

DELIVER P.D.D. IN 'USE FIXTURE IDEIII- im: ASSOCIATION IIIIIR E IFICATIONTO RETRIEVE FABRICATION PROGRAN FIXTURE IDENTIFICATION POSITION DEFINING DAWSTANDARD P05) TO MEMORY 3 DATA FROM IIEIIDRIIs FRO" STORAGE 46 DELIVER POSITION DELIVER STANDARD P05 DEFINING DATA T0 FAB. PROGRAM TO COMPUTING ELEMENT 45 COMPUTING EIEIIEIII 4s COMPUTE ACTUAL POSITION FABRICATION PROGRAM DATA (FIG. 24)

PATENTEOJMI 4m:

FTC-3.23

FLOW CHART OF MEASUREMENT STATION COMPUTING ELEMENT 24 SHEET 17 OF I 8 INT DATA aleaalou FROM CONTROL ELEMENT qr "st qr sI AND STORE' EQUATIONS (n (2) (a I EXIT I FIND P [O IOI-IIZI' FIND P I STORE POSITION DEFINING DATA PATENTED JAN "4 I972 SHEET 18DF I8 ENTER INTO PROGRAM ELEMENT 46 PART f I I READ DIRECTION cosmEs OF NORMAL ""AIPIIIIIII 22212 2: N Lqr; Nqr, Nqr, EST RSI, RS1, con uT z STORE OQ O 0 in 112 in 1 x' y' "21 "22 "25 y- Xc Y0 Z0 62 EQUATIONS (MI-(a5) L m N Ls M8 READ POSITION DEFINING um I FROM MEMORY3 01 0! 01 COMPUTE ORIENTATION CORRECTION FACTORS A STORE sinC,cosC, a u m E05. (128) (129) (11) (an (85) READ comm) mom V I6 2 PROGRAM ELEMENT 46 F 4 I COMPUTE TILT .4

FLOW CHART 0F FABRICATION STATION COMPUTE ROTATE 4 48-6 E0 (.31) OR (32) COMPUTE x',y;z' EOS. (II-(I13) COMPUTE x';y",z

Eos. (132)-(134) I SEND CORRECTED COMMAND TO CONTROL ELEMENT 44 READY FOR NEXT PART METHOD AND APPARATUS FOR PRECISELY CONTOURING A WORKPIECE IMPRECISELY POSITIONED ON A SUPPORTING FIXTURE BACKGROUND OF THE INVENTION Program-controlled machine tools establish the relative positions of the workpiece and the metalworking tool in response to a stored program so as to produce a precise contour on the workpiece. The stored program controls the sequence of motions of the workpiece and of the cutting head or other metalworking device. In all such program-controlled machine tools of the prior art, it has been necessary to position the workpiece precisely on a suitable support or fixture, which is in turn precisely positioned with respect to the cutting head.

Program-controlled machine tools, especially those of the type known as numerically controlled machine tools, are capable of producing precise contours within tolerance limits of 0.001 inch or smaller. In order to maintain the precision of the workpiece contour within such limits, the workpiece must be positioned on the fixture within limits of the same order of magnitude. The precise positioning of a workpiece by either manually or automatically controlled means within such fine limits is time consuming and presents a serious limitation on the output of such a program-controlled machine tool.

BRIEF SUMMARY OF THE INVENTION The methods and apparatus of the present invention allow an operator to place a workpiece on a fixture at a position anywhere within relatively wide tolerance limits (e.g., oneeighth or one-fourth inch) of a standard position. Such imprecise positioning can be easily and quickly accomplished manually or by power-operated means. According to the present invention, the program of the machine tool is modified in accordance with the difference between the actual position of the workpiece on its fixture and the standard position, so that the machine tool produces precise contours on the workpiece within the same tolerance limits as if the workpiece were in its standard position.

A workpiece to be precisely machined according to the invention, must first have placed on it a plurality of precisely located datum marks, with respect to which the desired locations of the machine operations are known. In the embodiment described, these datum marks take the form of datum contours which may be formed on the workpiece by conventional, manually controlled machines. These datum contours may be either: (a) two nonparallel straight edges; or (b) three nonparallel planes, whose intersections need not be on the workpiece surface.

The workpiece, with the datum contours formed thereon, is placed on a fixture adapted to support the workpiece while it is being fabricated by one or more machine tools. The machine tool is controlled by a stored program, which, as stored, is effective to produce a finished product of the desired contour only if the workpiece has its datum contours in a predetermined standard position with respect to the fixture, and the fixture is accurately located in a predetermined position in the machine tool.

The workpiece is placed on the fixture in an approximate position, i.e., within predetermined limits of the standard position. These limits can typically permit rotational displacements of the workpiece, with respect to a center of rotation which is specified with respect to the fixture, such that angles of pitch, yaw, and tilt of up to 30 can be tolerated, while linear displacements, in each of three orthogonal directions, of up to one-quarter inch can also be tolerated. (The maximum size of the tolerance limits is a function of the distances between the workpieces surface discontinuitiesi.e., straight edges or surfaces-which are visible when looking down on a standard-oriented workpiece which is mounted on the fixture.) Thus, the placement of this workpiece in the fixture is easier to achieve than if positioning within, say, a tenthousandth-inch limit were required.

The fixture is then placed in an accurately located position with respect to a table in a measuring apparatus. The table is movable in orthogonal directions with respect to the base of the measuring apparatus. The measuring apparatus controls the movement of the table and also of a probe which is movable vertically to engage and disengage the surface of the workpiece. The table is controlled to produce a relative movement between the workpiece and the probe so that a downward projection of the probe position describes a predetermined path across the workpiece surface. At spaced points along that path, the probe is controlled to move downwardly and engage the working surface. Data defining the points where the probe encounters the datum contours are recorded. After a sufficient number of such points are located, that data determines precisely the position of the workpiece on the fixture. This position-defining data is used to compute correction data for modifying the machine tool program so that it will accurately command the desired machining operation on the workpiece in its actual position.

In the apparatus illustrated, the fixture carries identifying indicia which may be read visually or automatically. The probing operation is carried out at a measurement station and the fixture then travels on a conveyor to a fabrication station. Before a workpiece leaves the measurement station, its positiondefining data is stored in a memory in association with data identifying the fixture carrying that workpiece. When the fixture arrives at the fabrication station, the identifying indicia on the fixture is again observed, and is used to retrieve from memory the position-defining data, which is utilized to modify the tool program to produce the desired product.

Although only one fabrication station is illustrated, a more typical arrangement would include a plurality of such stations, connected by conveyors, and all having access to a common memory in which the position-correcting data for all workpiece-carrying fixtures are stored.

Alternatively, only one operating station may be employed, at which the measurement operation and one or more fabrication operations may be carried out.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a block diagram schematically illustrating apparatus embodying the invention;

FIG. 2 is a perspective view of a typical five-axis machine tool, such as may be controlled by the apparatus of this invention;

FIG. 3 is a somewhat diagrammatic elevational view of the measurement station illustrated in FIG. 1;

FIG. 4 is an elevational view on a greatly enlarged scale, showing one fonn of position probe which may be used in the measurement station of FIG. 3;

FIG. 5 is a perspective view of a workpiece illustrating four paths of movement which may be taken by the probe of FIG. 4 over the workpiece surface;

FIG. 6 is a graphical illustration of the relationship between two sets of coordinates U, V, W, and U, V, W, which are used in the analysis of the workpiece position;

FIG. 7 is a graphical illustration of the relationship between a set of coordinates X", Y", Z", fixed with reference to the machine tool of FIG. 2 and a set of coordinates X, Y, Z, fixed with respect to the fixture which supports the workpiece;

FIG. 8 is a graphical illustration showing the relationship between the two machine tool coordinates X", and Y" and two compensating coordinates X, Y

FIG. 9 is a graphical illustration, which cooperates with FIG. 8, and illustrates the relationship between compensating coordinates X, Z and the machine tool coordinates X", Z";

FIG. 10 is a graphical illustration of the angles whose cosines are used as direction cosines in fixing the orientation of the datum contours;

FIG. 11 is a graphical illustration of the midpoint of the mutual perpendicular to two nonintersecting lines, which midpoint is used as a reference point for locating certain workpieces; 

1. A method of precisely contouring a workpiece by controlling the components of a machine tool, said components comprising a table for supporting the workpiece, a working member for engaging the workpiece, and means for relatively moving the member and the table, including the steps of: a. precisely locating two nonparallel datum lines on a blank workpiece; b. fastening the workpiece on a fixture in a working position within a predetermined range of a standard position; c. measuring precisely the positions of at least two points on each of said lines on the fixture; d. computing from the measured positions a set of data defining the working position of the workpiece on the fixturE; e. recording data defining precisely an operation on a workpiece in the standard position on a fixture in a predetermined location on the machine tool table, said data including:
 1. a point on the workpiece to be aligned with said working member of the machine tool for engagement with said point by said member; and
 2. the direction of a plane to have a predetermined angular relationship with respect to said member when the working member contacts the workpiece at said point; f. precisely locating the fixture on the machine tool table in said predetermined position with the workpiece in its working position on the fixture; g. computing from the working position defining data and the operating defining data a set of instructions for the machine tool components to move said plane into said predetermined angular relationship and align said point with said working member of the machine tool; and h. controlling the machine tool components in accordance with said set of instructions.
 2. A method as defined in claim 1, in which said step of precisely locating two nonparallel datum lines is accomplished by machining edges on the workpiece, said edges constituting said nonparallel datum lines.
 2. the direction of a plane to have a predetermined angular relationship with respect to said member when the working member contacts the workpiece at said point; f. precisely locating the fixture on the machine tool table in said predetermined position with the workpiece in its working position on the fixture; g. computing from the working position defining data and the operating defining data a set of instructions for the machine tool components to move said plane into said predetermined angular relationship and align said point with said working member of the machine tool; and h. controlling the machine tool components in accordance with said set of instructions.
 2. relatively moving the workpiece and probe stepwise laterally of said rectilinear path;
 2. the direction of a plane to have a predetermined angular relationship with respect to said member when the member contacts the workpiece at said point; f. precisely locating the fixture on the machine tool in said predetermined position with the workpiece in its working position on the fixture; g. computing from the working position defining data and the operation defining data a set of instructions for the relatively moving means of the machine tool to move said plane into said predetermined angular relationship and align said point with said member of the machine tool; and h. controlling the relatively moving means of the machine tool in accordance with said set of instructions.
 2. computing position defining data from the location of said indicia; c. preparing data for an operation on a workpiece in said standard position on a fixture mounted in a predetermined position on said machine tool table; d. placing the workpiece on a fixture within said predetermined range of said standard location; e. placing said fixture in a predetermined position relative to said measurement station; f. measuring the location of said indicia on the fixture; g. computing position defining data from the measurement of the indicia; h. storing the position-defining data; i. computing from the position-defining data and the fabrication data a set of instructions for the position-changing means of the machine tool; j. placing the fixture on the machine tool table in a predetermined position; k. controlling the position-changing means in accordance with said set of instructions.
 2. the direction of a plane to be perpendicular with respect to said member when the member contacts the workpiece at said point; f. precisely locating the fixture on the machine tool table in said predetermined position with the workpiece in its working position on the fixture; g. computing from the working position-defining data and the operation-defining data a set of instructions for the machine tool to rotate and tilt said table and thereby to move said plane into said perpendicular relationship, and to move said table along said mutually perpendicular axes to align said point with said working member of the machine tool; and h. controlling the relatively moving means of the machine tool in accordance with said set of instructions.
 3. repeating step (1) and comparing the distance measurement with that of step (1); and
 3. The method as defined in claim 1, in which the datum lines are edges on the workpiece and in which the step of measuring precisely the positions of the edges is accomplished by relatively moving the workpiece and a probe so that the probe traces along the workpiece a plurality of paths which intersect each of the edges at least twice, and recording the positions of said intersections.
 4. A method as defined in claim 1, in which each of the two nonparallel datum lines is the intersection of two nonparallel planes formed on the workpiece.
 4. repeating steps (2) and (3) until a sudden change in the comparison of said distance measurements indicates that an edge has been encountered by the probe.
 5. A method of precisely contouring a workpiece by controlling the movements of a machine tool having a table for supporting the workpiece, a working member for engaging the workpiece, and means for relatively moving the member and the table, including the steps of: a. precisely locating datum-defining indicia on the workpiece; b. fastening the workpiece on a fixture in a working position within a predetermined range of a standard position; c. measuring precisely the positions relative to the fixture of at least three points on said indicia to determine the working position of the workpiece on the fixture; d. computing from the measured positions a set of data defining the working position of the workpiece on the fixture; e. recording data defining precisely an operation on a workpiece in the standard position on a fixture in a predetermined location on the machine tool, said data including:
 6. The method of claim 5, in which said step of measuring precisely step comprises: a. relatively moving the workpiece and an indicia-recognizing probe in accordance with a second recorded program so that the probe follows a path which intersects said indicia if said workpiece is located within said range; b. recording the location of said intersection; and c. repeating said relatively moving and recording steps to tRace different paths until a sufficient number of intersections are located to define completely the position of the workpiece.
 7. The method of claim 6, in which: a. said indicia comprise two nonparallel edges on the workpiece; and b. the step of relatively moving the workpiece and the probe is accomplished by:
 8. The method of claim 6, in which: a. said indicia comprise two planes on the workpiece; and b. the step of relatively moving the workpiece and the probe comprises, for each of said planes, the steps of moving an array of at least three probes along parallel rectilinear paths toward said plane until contact with the plane is made by all three probes, said three points of contact establishing the location of the plane; c. said recording step comprises, for each plane, recording all three positions at which the probes contact the plane, said three positions being effective to define completely the position of the plane.
 9. A method of contouring a workpiece on a machine tool having a table for supporting the workpiece, a tool holder, and means for changing the relative positions of the table and tool holder, including the steps of: a. applying datum defining indicia to the workpiece; b. preparing and storing a program for:
 10. The method of claim 9, including the steps of: a. preparing and storing a plurality of measurement station programs for a corresponding plurality of different types of workpieces; b. selecting, for each workpiece, a particular measurement station program from said plurality; c. preparing a plurality of sets of fabrication station data for a corresponding plurality of different types of workpieces; d. selecting, for each workpiece, a particular set of fabrication station data from said plurality of sets.
 11. A method of precisely contouring a workpiece by controlling a machine tool having a table for supporting the workpiece, a working member for engaging the workpiece, and means for relatively moving the work-engaging member and the table, said last means including means for independently moving said table relative to the member in each of three mutually perpendicular directions, means for rotating the table about an axis parallel to one of said directions, and means for tilting the table about a second axis parallel to another saiD direction, including the steps of: a. precisely locating datum-defining indicia on a blank workpiece; b. fastening the workpiece on a fixture in a working position within a predetermined range of a standard position; c. measuring precisely the positions relative to said fixture of a plurality of points on said indicia to determine the working position of the workpiece or the fixture; d. computing from the measured positions a set of data defining the working position of the workpiece on the fixture; e. recording data defining precisely, for a workpiece in the standard position on a fixture in a predetermined location on the table said data comprising:
 12. The method of claim 11, wherein said indicia comprise two nonparallel edges on the workpiece, and said measuring step includes the measurement of the positions of at least two points on each edge.
 13. The method of claim 11, wherein said indicia comprise two nonparallel planes on the workpiece, and said measuring step includes the measurement of at least three points on each plane. 